Can I get help with this graph? It involves derivatives and differentiation. I got h'(2) right but need help with h'(1) and h'(3)

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Answer 1 · 2018-06-13T16:38:00

Given that $h (x) = f (x) \cdot g (x)$ $h(x) = f(x) * g(x)$ , we know from the product rule that $h'(x) = f'(x)g(x) + f(x)g'(x)$ .

Therefore

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

The values of $f'(1)$ and $g'(1)$ will be determined by taking the slope of the graphs at those points.

$f'(1) = (3 - 0)/(2- 0) = 3/2$
$g'(1) = (1 - 0)/(0 - 4) = -1/4$

To determine the values of $f(1) and g(1)$ , knowing the equation of the lines would be helpful.

For f(x): $y - 0 = 3/2(x - 0) -> y = 3/2x$
For g(x): $y - 1 = -1/4(x - 0) -> y = -1/4x + 1$

Therefore

$f(1) = 3/2(1)= 3/2$
$g(1) = -1/4(1) + 1 = 3/4$

Piecing all this together:

$h'(1) = 3/2(3/4) + (-1/4)(3/2) = 9/8 - 3/8 = 6/8 = 3/4$

The same process is required for $h(3)$ . I'll leave that up to you.

Hopefully this helps!