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
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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)
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