Please help me with the following questions!

Let f(x) = (x -3)2+4x - 4. Find its critical number and Let f(x) be a function that is differentiable for all x E R. As it critical value. If the function has no critical number, enter DNE is differentiable, it must also be continuous, and hence the for both answers. Mean Value Theorem applies. The function has a critical number at c = Suppose that f(x) is even. Using the Mean Value Theorem, and its critical value is f(c) = you can conclude that for any non-zero c E R, there must exists a b E (-c, c) such that f'(b) = Consider the function f(x) = 4(sin x + cos x) with domain Suppose instead that f(x) is odd. Using the Mean Value x E (0, TC). Find the interval over which the function is Theorem, you can conclude that for any non-zero c E R, concave up. 2 there must exists a b E (-c, c) such that f'(b) = f(x) is concave up over the interval 5 Find the absolute minimum and maximum values of Find the inflection point (Xp, f(xp )) of the following function: f(x) = x - In x over the interval [1/2, 3]. f(x) = 5x3 + 15x2 - x + 9. If an inflection point does not exist, enter DNE for both answers. Minimum value: Xp Maximum value: 6 f ( x p ) = 3 Find the location of the local minimum and local maximum of X 2 the function f(x) = x - 3 4 The local minimum is located at x = The local maximum is located at x