Application of Derivatives2 passages

Application of Derivatives — JEE Maths Comprehension Passages & Solutions

2 reading-comprehension sets on Application of Derivatives with full step-by-step solutions, including past-year (PYQ) passages. Free to practice.

hard
Let f(x)f(x) be a thrice differentiable function on the interval [a,e][a, e]. Define the auxiliary functions: G(x)=[f′(x)]2+f(x)f′′(x),H(x)=e−x(f′(x)−f(x))G(x) = [f'(x)]^2 + f(x)f''(x), \qquad H(x) = e^{-x}(f'(x) - f(x)) It is given that f(a)=f(e)=0f(a) = f(e) = 0. For constants b,c,db, c, d satisfying a<b<c<d<ea < b < c < d < e, the function takes the values f(b)=2f(b) = 2, f(c)=−1f(c) = -1, and f(d)=2f(d) = 2.
Read passage →
medium
If f:R→Rf : \mathbb{R} \to \mathbb{R} is a function defined by f(x)=2cos⁡22x+34sin⁡4x+ax,f(x) = 2\cos^{2}2x + \frac34\sin 4x + ax , where a∈Ra \in \mathbb{R}.
Read passage →

Practice Application of Derivatives comprehension

Sign up free to solve Application of Derivatives comprehension sets with instant step-by-step solutions, bookmarks, and progress tracking on doMath.

Sign up freeExplore doMath