Application of Derivatives questions
910 published questions with worked solutions.
- What is the length of the longest interval in which the function f(x)=2 ^2x-1 is decreasing?
- If A and B are acute angles such that 2A+2B= , then what is the maximum value of A. B?
- ABC is a triangle right angled at B. If AC=8 units, then what is the area of the triangle of maximum area?
- For the curve y=xe^ 2x
- Let f(x)= xe^x ,dx. Then f(x) decreases in the interval
- The curve y=-x^3+3x^2+2x-27 has the maximum slope at
- If x+y=20 and P=xy, then what is the maximum value of P?
- What is the maximum value of 2x 2x?
- Consider the following statements in respect of the function f(x)= x : 1. f(x) increases in the interval (0, ). 2. f(x) decreases...
- Let p, q and 3 be respectively the first, third and fifth terms of an AP. Let d be the common difference. If the product (pq) is...
- For what value of , where 0< < 2 , does + attain maximum value?
- What is the slope of the tangent of y= ^ -1 ( x) at x=- 4 ?
- Consider the following statements in respect of the function f(x)=x^2+1 in the interval (1, 2) : 1. The maximum value of the...
- Where does the tangent to the curve y=e^x at the point (0, 1) meet x-axis?
- Consider the following statements in respect of the function f(x)=x+ 1 x : 1. The local maximum value of f(x) is less than its...
- What is the maximum area of a rectangle that can be inscribed in a circle of radius 2 units?
- What is the condition that f(x)=x^3+x^2+kx has no local extremum?
- If the function f(x)=x^2-kx is monotonically increasing in the interval (1, ), then which one of the following is correct?
- The tangent to the curve x^2=y at (1, 1) makes an angle with the positive direction of x-axis. Which one of the following is...
- Consider all rectangles lying in the region (x, y) R R : 0 x 2 and 0 y 2 (2x) and having one side on the x-axis. The area of the...
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