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Math  /  Calculus

QuestionGiven the function f with domain [−1,1], such that f(−1)=−1, f(−12)=−2, f′(−12)=0, and f′′(x)>0 on (−1,1).\text{Given the function } f \text{ with domain } [-1, 1], \text{ such that } f(-1) = -1, \, f\left(-\frac{1}{2}\right) = -2, \, f^{\prime}\left(-\frac{1}{2}\right) = 0, \text{ and } f^{\prime \prime}(x) > 0 \text{ on } (-1, 1). \text{Curve sketch the function } f.

Studdy Solution
Our sketch shows a curve starting at (−1,−1)(-1, -1), dipping down to a minimum point at (−12,−2)\left(-\frac{1}{2}, -2\right) with a horizontal tangent, and then curving upwards, remaining concave up, until x=1x = 1.

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