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- 1. What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the function f (x) = x² - x on the interval [-2,2]? 3. Given the interval [ -2,2] for the function f (x) = -8x² + 2x⁴ ; at which value/s of x will the maximum point occur?Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 3x + 10), [−2, 1]How did the function f(x) = -x^3 + e^x - 8 satisfy the intermediate value theorem? Show that f has a real zero on [-2, 1] using intermediate value theorem.
- Find the local and absolute maximum and minimum values of f(x) f(x) = cos x, x ∈ [-3pi/2 , 3pi/2 ].Find the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]Let f(x)= √6-x . Compute f'(2) using the limit definition. f'(2)= -1/4 Find an equation of the tangent line at x=2 y= ? How to solve for the equation of the tangent line at x=2?
- If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a <b. Then f(a) =f(b) = ________ ? Since f is continuous on the interval [-3,-1] and differentiable on the interval (-3,-1), by Rolle's Theorem there would exist a point c in interval (a, b) so that f'(c)= 0. However, the only solution to f '(x)= 0 is x= ________ , which is not in the interval (a,b) or in [-3,-1]. Thus, f cannot have more than one root in [-3,-1]. What would the blank be?Find the absolute maximum and minimum of f(x)=3x^3-x+1 on the interval [0,1]What is the minimum value of F(x) = -4 sin x? -4 -2 -1