Application of Derivatives
Find the intervals in which the following functions are strictly increasing or decreasing:(a) x2+2x−5 (b) 10−6x−2x2 (c) −2x3−9x2−12x+1 (d) 6−9x−x2(e) (x+1)3(x−3)3
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An open box with a square base to be made out of a given cardboard of area c2 (square) units. Show that the maximum volume of the box is 63c3 (cubic units.)
Find the approximate value of f(5.001), where f(x)=x3−7x2+15.
Using differentials, find the approximate value of :49.5
Show that the function given by f(x)=3x+17 is strictly increasing on R.
Find the equation of all lines having slope -1 that are tangents to the curve y=x−11,x=1.
Find the maximum of minimum values, if any, without using derivation, of the functions:−(x−3)2+9
Show that f(x)=x(x−5)2 satisfies Rolle's theorem on [0,5] and that the value of c is (35)