MHT-CET Application of Derivatives — practice questions
24 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Application of Derivatives in the app →The **slope of the tangent** to the curve $y = f(x)$ at point $(a, f(a))$ is:A function $f$ is **strictly increasing** on an interval if, on that interval:At a **local maximum** of a differentiable function $f$:The slope of the tangent to $y = x^3 - 3x + 1$ at $x = 2$ is:$y = x^3 - 6x^2 + x + 3$. The tangent is parallel to the line $y = x + 5$ at points where $x$ equals:Water is poured at $36\,\text{m}^3/\text{s}$ into a cylindrical vessel of base radius 3 m. The rate at which wIf $f(x) = x^2 - 4x + 3$, the **interval** on which $f$ is decreasing is:Find the approximate value of $ qrt{25.5}$ using differentials (given $ qrt{25} = 5$):**Lagrange's Mean Value Theorem (MVT)** states: for $f$ continuous on $[a,b]$, differentiable on $(a,b)$, ther$f(x) = 2x^3 - 3x^2 - 12x + 5$. The **local maximum value** occurs at:A 13-m ladder leans against a wall. Its top slides down at 0.5 m/s. When the foot is 5 m from the wall, the foThe function $f(x) = x^3 - 3x + 1$ has critical points at:Find the **maximum value** of $f(x) = in x + \cos x$ for $x \in [0, 2\pi]$.A rectangle is inscribed in a semicircle of radius $R$ with base on the diameter. The **maximum area** is:Find the **shortest distance** from origin to the curve $xy = 4$ (in the first quadrant):If $y = a \ln x + b x^2 + x$ has extreme values at $x = 1$ and $x = 2$, then $(a, b)$ is:The function $f(x) = \dfrac{x}{1 + x^2}$ attains its maximum value on $[0, \infty)$ at:If $f(x) = x^x$ for $x > 0$, then $f$ has a minimum at $x = $:A car moves so that its position $s(t) = 3t^3 - 12t^2 + 5$ (m, t in s). The time at which the car comes to **mTangent to the curve $y = qrt x + qrt y = c$ (where $c > 0$) at any point on it makes equal intercepts on thThe volume of a sphere is increasing at $8\pi$ cm³/s. The rate of change of surface area when the radius is 2 If the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, then $a$ equals:Find $ in 31°$ using approximation (given $ in 30° = 0.5$, $\cos 30° = qrt 3/2 \approx 0.866$, $1° = 0.01745$A wire of length $L$ is bent to form a rectangle. The **maximum area** enclosed is: