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Let F f+g, where the graphs of f and g are shown in the figure to the right. Find the followingderivative.F'(3)y=f(x)4y = gxF'(3)

Question
Let F f+g, where the graphs of f and g are shown in the figure to the right. Find the following
derivative.
F'(3)
y=f(x)
4
y = gx
F'(3)
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Let F f+g, where the graphs of f and g are shown in the figure to the right. Find the following derivative. F'(3) y=f(x) 4 y = gx F'(3)

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Step 1

It is known that, the slope of the function at a point is equal to the derivative of the function at the same point.

The derivative of the function f(x) at x = 3 is calculated as follows.

Vy
f(3)x
f(1.5)-f(5)
1.5-5
8-1
-3.5
7
3.5
=-2
l
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Vy f(3)x f(1.5)-f(5) 1.5-5 8-1 -3.5 7 3.5 =-2 l

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Step 2

The derivative of the function g(x) at x = 3 i...

g (3) Vy
Vx
g (5)-g(0)
5 0
6 1
5
5
=1
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g (3) Vy Vx g (5)-g(0) 5 0 6 1 5 5 =1

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Tagged in

Math

Calculus

Derivative

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