Question

If f(5) = 2, f′(5) = 3, g(5) = 4, and g′(5) = 1, find h(5) and h′(5), where h(x) = 3f(x) 2g(x).

Answer 1

To find h(5), substitute the known values of f(5) and g(5) into the function h(x), yielding h(5) = -2. For h'(5), apply the derivatives f'(5) and g'(5) with respect to the function h(x), resulting in h'(5) = 7.

Step-by-step explanation:

Given that h(x) = 3f(x) - 2g(x), we want to find h(5) and h'(5). Since we know f(5) = 2 and g(5) = 4, we can directly substitute those values to find h(5):

h(5) = 3f(5) - 2g(5) = 3(2) - 2(4) = 6 - 8 = -2.

To find h'(5), we will use the product rule and the given derivatives f'(5) = 3 and g'(5) = 1:

h'(x) = 3f'(x) - 2g'(x)