(g) Explain whether every local maximum and minimum of h occurs where h' equals zero or does not exist. (h) Explain whether h has a local maximum or minimum everywhere h' equals zero or does not exist.
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Can you do g and h please
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- For what values does x have a local minimum for this equation?Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11)2. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?
- Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local minimum at x = 3 and alocal maximum at (-1, -2).Let f(x)=kx^-1+x^2 For what values of k, function f(x) has a relative minimum but not a relative maximum?Calculate the difference d between the global maximum and global minimum values of f(x)=x2−4x+6 in the interval [−2,4].
- Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection point at (1, 11).For a certain function, f'(x) = 0 and f' (x) > 0 for -1 < x < 2. Which statement is not true? a) (2, f (2)) is a local maximum b) (2, f (2)) is a critical point c) 2, f (2)) is a local minimum d) (2, f (2)) Is a turning pointFind the value of x at which the absolute minimum occurs (if it exists) for the function f(x) = -x2 + 3x - 2 over the interval [1, 3].