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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.7 The Fundamental Theorem and Its Applications, #46 · Calculus · Integrals

The mountain … has an area … above the … axis

The mountain $y = - x^{2} + t$ has an area $A (t)$ above the $x$ axis. As $t$ increases so does the area. Draw an $x y$ graph of the mountain at $t = 1$ . What line gives $d A / d t$ ? Show with words or derivatives that $\frac{d ^{2} A}{d t ^{2}} > 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.7 The Fundamental Theorem and Its Applications, #46

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