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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?arrow_forwardFind aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2 {ax+b, x is greater than or equal to -2 is both continuous and differentiable.arrow_forwardFind the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]arrow_forward
- Solve for the derivative of the given functions using the Chain Ruleformula. Let f(x) = √(x2 + 3x + 1). Find f′(x). a.) What is the inner and the outer functions?b.) What is the derivative of the inner function?c.) What is the derivative of the outer function evaluated at the inner function?arrow_forwardIn the function: f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?arrow_forwardLet ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) = g(x) and ƒ′′(x) = -ƒ(x). Let h(x) = ƒ2 (x) + g 2(x). If h(0) = 5, find h(10).arrow_forward