Class 12

Math

Calculus

Application of Derivatives

The lengths of the sides of an isosceles triangle are $9+x_{2},9+x_{2}$and $18−2x_{2}$units. Calculate the area of the triangle in terms of x and find the value of x which makes the area maximum.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find both the maximum value and the minimum value of $3x_{4}−8x_{3}+12x_{2}−48x+25$ on the interval [0, 3].

Let f be a function defined on [a, b] such that $f_{prime}(x)>0$, for all $x∈(a,b)$. Then prove that f is an increasing function on (a, b).

The line $y=mx+1$is a tangent to the curve $y_{2}=4x$if 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 $f(x)=x_{2}+ax+1$is 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 $2x_{3}−24x+107$ 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 $C(x)=0.007x_{3}−0.003x_{2}+15x+4000$. Find the marginal cost when 17 units are produced