Question

The graph of a function, f is shown above. Let h(x) be defined as
h(x) = (x + 1) · f(x). Find h′(4).

Answer 1

Answer:

A

Step-by-step explanation:

We are given the graph of f and the function:

$h(x)=(x+1)\cdot f(x)$

And we want to find h'(4).

Therefore, we will differentiate both sides:

$\displaystyle h'(x)=\frac{d}{dx}\Big[(x+1)\cdot f(x)\Big]$

Use the product rule:

$\displaystyle h'(x)=\frac{d}{dx}(x+1)f(x)+(x+1)\frac{d}{dx}[f(x)]$

Differentiate:

$h'(x)=f(x)+(x+1)f'(x)$

Thus:

$h'(4)=f(4)+(4+1)f'(4)$

For f'(4), this is the derivative of f at x = 4. We can see that the derivative at this point is -2 as it is a line with a slope of -2.

And using the graph, f(4) is 4.

Therefore:

$h'(4)=4+(5)(-2)=4-10=-6$

The answer is A.