Question

Help pleaseee really dont know how to start with this​

Answer 1

Answer:

Slope is positive for all x, so always increasing

Step-by-step explanation:

Increasing/decreasing depends on the slope of the function, which is f'

f'(x) = 9x² + 18x + 25

If f'(x) > 0 for all x, then his claim is correct (increasing for all x)

If there's even 1 x-value for which f'(x) is not positive, his claim is incorrect

f'(x) is a quadratic function.

9x² + 18x + 25

9(x² + 2x) + 25

9(x² + 2(x)(1) + 1² - 1²) + 25

9(x + 1)² - 9 + 25

9(x + 1)² + 16

Since the minimum value of f' is 16, it's always positive.

Hence, the claim is correct