Math Problem Statement
Consider the function f(x)=3/4x^4-x^3-9x^2+20 (a) Find f(-2) (b) Find f'(x) The graph of the function f has a local minimum at the point where x=-2 (c) Using your answer to part (b), show that there is a second local minimum at x = 3
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Critical Points
Second Derivative Test
Formulas
Power rule: d/dx(x^n) = nx^(n-1)
Second derivative test: If f''(x) > 0 at a critical point, it is a local minimum
Theorems
Second Derivative Test
Suitable Grade Level
Grades 11-12
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