In Exercises 27-32, find the values of
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- Consider the general equation of a quadratic function: f(x)=ax2+bx+cf(x)=ax2+bx+c (Recall: aa, bb, and cc represent constants). Use the derivative f′(x)f′(x) to find the critical value of f(x)f(x) in terms of aa and bb (does this formula look familiar?) Use the second-derivative test to show that the critical value is a local maximum if a<0a<0 or a local minimum if a>0a>0. What determines whether the graph of f(x)f(x) is concave up or concave down? Does the graph of f(x)f(x) have any inflection points? Explain.arrow_forwardA-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.arrow_forwardFind the linearization L(x) of the function at a. f(x) = x3 − x2 + 9, a = −2arrow_forward
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