How do you determine whether the function h′(x)=(x2)−2x is concave up or concave down and its intervals?

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turtletalk75 · Accepted Answer

Step 1Find the derrivaive to the given functionIt will be 1+2x2For every integer value of x the value decreasesslope of the function f(x) i.e. f′(x) here the f is h′So as value of h is decreasingThe function h′(x) is concave up

Neunassauk8 · Accepted Answer

Step 1Investigate the sign of the second derivative.f(x)=x2−2x may be easier to differentiate if we write it asf(x)=x−2xf′(x)=1+2x2 andf″(x)=−2x3So,f″(x) is positive and the graph of f is concave up on (−∞,0)andf″(x) is negative and the graph of f is concave down on (0,∞)Because f is not defined at 0, there is no point of the graph at which th econcavity changes. (I.e. there is no inflection point)

How do you determine whether the function h'(x)=\frac{(x^{2})-2}{x} is concave

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New Questions in Calculus 1