MAC 2311 Midterm: Exam Study Guide
3 May 2018
School
Department
Course
Professor
1
x
Exam 2(Review Questions)
Find an equation for the tangent to the curve at the point.
1) f(x) = 4 - x + 1, (64, 1)
Solve.
2)
F ind the points where the graph of the funct ion have horizontal tangents.
f(x) = 2x3 - 15x
3)
F ind an equation of the tangent to the curve f(x)= that has s lope1 .
4
Find the derivative of the given function.
4)
s = t4 tan t -
Find the indicated derivative.
8)
F ind y
'''
if y = 5x sin x.
The equation gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds).
9)
s = 6 sin t - cos t
Find the body's velocity at time t= n/4 sec.
Find the derivative of the function.
10) y = (x + 1)2(x2 + 1) -2
11)
x + 4
t
h(x) = cos x 5
1 + sin x
2
Find dy/dt.
12) y = cos3(nt - 10)
13)
Find y
''
.
14) y = 5 sin(4x + 8)
Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values o
x. Find the derivative with respect to x of the given combination at the given value of x.
15)
f(x) + g(x), x = 3
15)
g(x + f(x)), x = 3
Use implicit differentiation to find dy/dx.
17) 3xy - 2y2 = 5
18) xy + x + y = x2 y2
19) cos xy + x3 = 5y3
20) e2x = sin(x + 4y)
Use implicit differentiation to find dy/dx and d2y/dx2.
21) 2y - x + xy = 6
22) 3x2 + 4y2 = 9
Solve
23) Find the slope of the curve 3xy3 - x5
y2 = -4 at ( -1, 2).
24) A t the t wo points where the curve x2 - xy + y2 = 25 crosses the x -axis, the tangents to the curve are
parallel. What is the common slope of these tangents?
Find the derivative of y .
25) y = 4x5
ln x - 1 x3
3
y = ecos(t/4) 4
x f(x) g(x) f '(x) g '(x)
1
8 5
5 -5
x f(x) g(x) f
'(x) g '(x)
3 1 9 6 5
4 3 3 5 -4
Document Summary
Find an equation for the tangent to the curve at the point: f(x) = 4 x. Solve: f ind the points where the graph of the funct ion have horizontal tangents. f(x) = 2x3 - 15x, f ind an equation of the tangent to the curve f(x)= x + 4 that has s lope. Find the derivative of the given function: s = t4 tan t - t. Find the indicated derivative: f ind y """ if y = 5x sin x. The equation gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds): s = 6 sin t - cos t. Find the body"s velocity at time t= n/4 sec. Find the derivative of the function: y = (x + 1)2(x2 + 1) -2 h(x) = cos x 5. Find dy/dt: y = cos3(nt - 10) y = ecos(t/4) 4. Find y"" : y = 5 sin(4x + 8)
