Question

find the intervals on which f(x) is increasing.the intervals on which f(x) is decreasing and the local extrema f(x)= 2x⁴+24x³+33​

Answer 1

EXPLANATION.

→ f(x) = 2x⁴ + 24x³ + 33

→ To find the intervals in which f(x) is increasing.

→ To find the intervals in Which f(x) is decreasing.

→ equation → f(x) = 2x⁴ + 24x³ + 33

→ Differentiate the equation.

→ f'(x) = 8x³ + 72x² + 0 = 0

→ f'(x) = 8x² ( x + 9 ) = 0

→ f'(x) = points are = 0,-9

→ put the point in the wavy curve method.

→ assume any point greater than 0 and put

in the following equation.

→ we can see that the point become positive.

→ f'(x) is ↑ in intervals → ( - ∞ , -9) U ( 0,∞ )

→ f'(x) is ↓ in intervals → ( -9, 0)