Application of Derivatives
The lengths of the sides of an isosceles triangle are 9+x2,9+x2and 18−2x2units. Calculate the area of the triangle in terms of x and find the value of x which makes the area maximum.
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Find both the maximum value and the minimum value of 3x4−8x3+12x2−48x+25 on the interval [0, 3].
Let f be a function defined on [a, b] such that fprime(x)>0, for all x∈(a,b). Then prove that f is an increasing function on (a, b).
The line y=mx+1is a tangent to the curve y2=4xif the value of m is(A) 1 (B) 2 (C) 3 (D) 21
Find the least value of a such that the function f given by f(x)=x2+ax+1is strictly increasing on (1,2)˙
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Find the maximum and minimum values of f , if any, of the function given by f(x)=∣x∣,x∈R.
Find the maximum value of 2x3−24x+107 in the interval [1, 3]. Find the maximum value of the same function in [3,1]˙
The total cost C (x) in Rupees associated with the production of x units of an item is given by C(x)=0.007x3−0.003x2+15x+4000. Find the marginal cost when 17 units are produced