let-gx2xt2t1t5-dt-gx-int2x-t2t-1t-5-dt-find-the-critical-points-of-gx-gx-and-det

Question

Let g(x)=∫2xt2(t−1)(t−5) dtg(x)=\$$int_2$$^{x}$$t^2(t-1)(t-5$$)\,dt. Find the xx-coordinates of the critical points of g(x) g(x)  and determine the intervals where g g  is increasing or decreasing.

Accepted Answer

Critical points at x={0,1,5}x=\left\lbrace0,1,5\right\rbraceIncreasing on x∈(−∞,1)∪(5,∞)x\in\left(-\infty,1\right)\cup\left(5,\infty\right)Decreasing on x∈(1,5)x\in\left(1,5\right)

Answer

Critical points at x={0,1,5}x=\left\lbrace0,1,5\right\rbraceIncreasing on x∈(−∞,0)∪(5,∞)x\in\left(-\infty,0\right)\cup\left(5,\infty\right)Decreasing on x∈(0,5)x\in\left(0,5\right)

Answer

Critical points at x={1,5}x=\left\lbrace1,5\right\rbraceIncreasing on x∈(−∞,1)∪(5,∞)x\in\left(-\infty,1\right)\cup\left(5,\infty\right)Decreasing on x∈(1,5)x\in\left(1,5\right)

Answer

Critical points at x={1,5}x=\left\lbrace1,5\right\rbraceIncreasing on x∈(−∞,1)∪(1,5)x\in\left(-\infty,1\right)\cup\left(1,5\right)Decreasing on x∈(5,∞)x\in\left(5,\infty\right)

Let g(x)=∫2xt2(t−1)(t−5)dtg(x)=\(\int\)_2^{x}t^2(t-1)(t-5)\,dt. Find the xx-coordinates of the critical points of g(x) g(x) and determine the intervals where g g is increasing or decreasing.

Let $g (x) = \int_{2}^{x} t^{2} (t - 1) (t - 5) d t$ . Find the $x$ -coordinates of the critical points of $g (x)$ and determine the intervals where $g$ is increasing or decreasing.