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10 Nov 2019

a) Find an equation of thetangent line to the graph of y = g(x) at x=5 if g(5)= -3 and g'(5)=4.

b) If the tangent line line to y=f(x) at (4,3) passes through thepoint (0,2), find f(4) and f '(4).

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Keith Leannon
Keith LeannonLv2
3 Apr 2019

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If the tangent line to y=f(x) at (4,3) passes through the point (0,2) find f(4) and f'(4).

Assume f and g are differentiable functions with h(x)=f(g(x)).Suppose the equation of the line tangent to the graph of g at thepoint (5,6) is y=4x-14 and the equation of the line tangent to thegraph of f at (6,9) is y=-2x+21.
Calculate h(5) and h'(5)
Determine an equation of the line tangent to the graph of h at thepoint on the graph where x=5
1) a- find the slope of the tangent to the curve y= 3 + 4x^2- 2x^3at the point where x=a
b- find the equations of the tangent lines at the points (1,5) and(2,3)
c- Graph the curve and both the tangent on a common screen

2) if a rock is thrown upward on the planet mars with a velocity of10 m/s, its height( in feet) after t seconds is given by h= 10t-1.8t^2
a-find the velocity of the rock after one second
b- find the velocity of the rock when t = a
c-when will the rock hit the surface
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3) a-find an equation of the tangent line to the graph of y= g(x)at x =5 if g(5)=-3 and g'(5)=-4
b-if the tangent like to y = f(x) at (4,3) passes through the point(0,2) find f(4) and f'(4)

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