MATH 1A Lecture 12: MATH 1A – Lecture 12 – 2.8 Derivative as a Function.docx

Let f(x) = sin(a). Sketch the graph of f over the interval x epsilon [-pi/2, pi/2]. Use a 1-1 scale (1 unit in the horizontal is as long as 1 unit in the vertical). Estimate the slope of the line tangent to the graph at x0 = 0 as follows. Make a table whose first row contains a set of values of h (of your choice) approaching zero, and whose second row contains the slopes of the secant lines through (x0, f(x0)) and (x0 + h, f(x0 + h)). Then state the estimated limiting tangent slope. Find the equation for the tangent line to the graph of f at x = x0. Add a sketch of the tangent line and one sample secant line for one value of h in your figure in (a). Let f(x) = x3/2. Sketch the graph of f over the interval x epsilon [0, 2]. Use a 1-1 scale. Estimate the slope of the line tangent to the graph at c = 1 as follows. Make a table whose first row contains a set of special values of x (of your choice) approaching c, and whose second row contains the slopes of the secant lines through (c, f(c)) and (x, f(x)). Then state the estimated limiting tangent slope. Find the equation for the tangent line to the graph of f at x = c. Add a sketch of the tangent line and one sample secant line for one special values of x in your figure in (a). Plot a graph of the given functions and find the given limit. Show the value of the limit on the y-axis in your graph. If the limit does not exist, explain why. g(x) = 2x + x2, lim x rightarrow -2 (2x + x2) g(h) = 2 - h/2, lim x rightarrow 1 (2 - h/2) h(t) = 1 - t2 / 1 - t, lim t rightarrow 1 1 - t2 / 1 - t f(x) - 1 / x - 1, lim x rightarrow 1 1 / x - 1

Consider the function f(x) = 13x - 2 We will take steps to find the tangent line to the graph of f azt the general point (x, f(x)), and use it to find a tangent line with a specific property. For my point (x, f(x)) on the graph. of f let (x + h, f(x + h)) be another point on the graph of f, where h 0. The slope of the (secant) line joining the two points (x, f(x)) and (x + h, f(x + h)) can be simplified to the form A / 13x - 2 + 13(x + h) - 2, where A is a constant. Find A. Answer. A = By considering the slope of the secant line as h approaches 0, find the slope of the tangent line to the graph of f at the point (x, f(x)) Answer. The slope of the tangent line to the graph of f at the point (x, f(x)) is . Note The correct answer should be an expression in x. At which point on the graph of f is the tangent line parallel to the line y = 13 / 10x? Answer. The tangent line to the graph of f at the point ( , ) is parallel to the line y = 13 / 10x.

Need Help?ReWalch Talk to a Tulb /1 points sCalcET8 3.4.007 Find the derivative of the function Fx) (3x6 + 4x3)4 F(x) = Need Help? Resd it Watch It Talk to a Tutor +1 points SCalcETS 3 4.009 Find the derivative of the function. f(x) = v 9x + 8 f (x) Read It Watch It Talk to a Tutor Type here to search

34.0 Find the derivative of the function /(x) = (2x-6)4(x2 + x + 1)5 f(x) Need Help? Read t

0/1 points I Previous Answers SCalcET8 3.4.031 Find the derivative of the function.E F(t) = e3tsin(2t) F(t) = | e 3tsin 2t (6t cos2+ 3 sin 2t ) | Need Help? L-Read it | | |L-Watchltー」11 Talk to a Tutor 9、0-11 points scalcET8 3 4 053 Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (r, 0) Need Help? aditWatch t Talk to a Tutor

-12 points SCalcET8 3.4.063 A table of values for f, g, f, and g' is given. xf(x) g(x) f'(x) g'(x) 2 4 6 7 9 2 3 2 (a) If h(x)=rg(x), find h'(3). h'(3) (b) If H(x) g(f(x), find H'(2). H(2) Need Help? Read It WatehTak to a Tutor Talk to a Tutor Submit Assignme

Write the composite function in the form Ag(x)). [Identify the inner function u = g(x) and the outer function y = ru).] 3 (g(x), f(u)) = ( | 277