Question

If h(x)=x^2/f(x) and f(3) = 2 and f'(3) = 4, then h' (3) = -12.

true
false​

Answer 1

FALSE.

Explanation:

Given:

• h(x)=x^2/f(x)
• f(3) = 2
• f'(3) = 4

To Find:

• Whether h'(3) = -12 or not.

Formula used:

• For a function y = f(x)/g(x), the differentiation of y is defined as y' = [f'(x)*g(x) - g'(x)*f(x)]/(g(x))^2. This is know as quotient rule of differentiation.

Using the above formula, we have

h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2

So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2

h'(3) = (12-36)/4

h'(3) = -24/4 = -6

So, h'(3) = -6 and not -12.

So, the given value is FALSE.