AP EAMCET · Maths · Differentiation
If \(f(x)=x^4-x^3+7 x^2+14\), then what is the value of \(f^{\prime \prime}(5)\) ?
- A 842
- B 248
- C 284
- D 482
Answer & Solution
Correct Answer
(C) 284
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^4-x^3+7 x^2+14\) \(\begin{aligned} & \Rightarrow f^{\prime}(x)=4 x^3-3 x^2+14 x \\ & \Rightarrow f^{\prime \prime}(x)=12 x^2-6 x+14 \\ & \therefore f^{\prime \prime}(5)=300-30+14=284 \end{aligned}\) Hence, option (c) is correct.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\vec{a}, \vec{b}\) are two unit vectors with \((\vec{a}, \vec{b})=\theta\) and \(|\vec{a}-\vec{b}|=1\), then \(2|\vec{a}+\vec{b}| \cos \frac{\theta}{2}=\)AP EAMCET 2023 Easy
- The solution of the differential equation \(\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0\), isAP EAMCET 2016 Medium
- In a \(\triangle A B C, 2 A+C=300^{\circ}\). If the circumradius of the \(\triangle A B C\) is eight times its inradius then \(\sin \frac{C}{2}=\)AP EAMCET 2025 Medium
- \(\int_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x=\)AP EAMCET 2024 Easy
- If are position vectors of respectively and if are mid points of sides and , then is equal toAP EAMCET 2021 Easy
- If \(f(x)=x^3+p x^2+q x\) is defined on \([0,2]\) such that \(f(0)=f(2)\) and \(f^{\prime}\left(1+\frac{1}{\sqrt{3}}\right)=0\), then \(p^2+q^2=\)AP EAMCET 2019 Medium
More PYQs from AP EAMCET
- Let \(\bar{a}=2 \bar{i}+3 \bar{j}+\bar{k}, \bar{b}=4 \bar{i}+\bar{j}, \bar{c}=\bar{i}-3 \bar{j}-7 \bar{k}\).
If \(\bar{r}=x \bar{i}+y \bar{j}+z \bar{k}, \bar{r} \cdot \bar{a}=9, \bar{r} \cdot \bar{b}=7, \bar{r} \cdot \bar{c}=6\) then \((x, y, z)=\)AP EAMCET 2022 Easy - If and thenAP EAMCET 2019 Medium
- All letters of the word 'AGAIN' are permuted in all possible ways and the words so formed (with or without meaning) are written as in a dictionary, then the \(50{ }^{\text {th }}\) word isAP EAMCET 2025 Medium
- If \(\Delta=a^2-(b-c)^2\), is the area of the \(\triangle A B C\), then \(\tan A\) is equal toAP EAMCET 2010 Easy
- Let \(A B C\) be a triangle. Let \(u=\mathbf{A B}\) and \(v=\mathbf{A C}\). If \(D\) is a middle point of \(B C\), then \(\mathbf{A D}=\)AP EAMCET 2020 Easy
- \(A, B, C\) and \(D\) are four different gases with critical temperatures \(304.1,154.3,405.5\) and \(126.0 \mathrm{~K}\) respectively. While cooling the gas, which gets liquefied first?AP EAMCET 2016 Easy