Question:
(e) Find the slope of the curve \( y = 2x^2 - 3\cos x \) at \( x = 0 \).
(e) Find the slope of the curve \( y = 2x^2 - 3\cos x \) at \( x = 0 \).
Show Hint
For slope, differentiate the function and substitute the given point.
Updated On: Mar 1, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
Differentiatethegivencurve:
\[
\frac{dy}{dx}=\frac{d}{dx}(2x^2-3\cosx)=4x+3\sinx.
\]
At\(x=0\):
\[
\frac{dy}{dx}=4(0)+3\sin(0)=0.
\]
Was this answer helpful?
0
0
Top Questions on Differential equations
- Let \( y = f(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that \( f(0) = 0 \). If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then \( \alpha^2 \) is equal to __________.
- JEE Main - 2025
- Mathematics
- Differential equations
- If \( x = f(y) \) is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with \( f(0) = 1 \), then \( f\left( \frac{1}{\sqrt{3}} \right) \) is equal to:
- JEE Main - 2025
- Mathematics
- Differential equations
- Find the shortest distance between the lines: \[ \vec{r} = 3\hat{i} + 3\hat{j} - 5\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k}), \] \[ \vec{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}). \]
- UP Board XII - 2024
- Mathematics
- Differential equations
The differential coefficient of the \( \sin(x^2 + 5) \) with respect to \( x \) will be:
- UP Board XII - 2024
- Mathematics
- Differential equations
- (d) If \( y = x^x \), then find \( \frac{dy}{dx} \).
- UP Board XII - 2024
- Mathematics
- Differential equations
View More Questions
Questions Asked in UP Board XII exam
State Gauss's Law in electrostatics. Using it (i) find electric field due to a point source charge \( q \) and (ii) deduce Coulomb's law between source charge \( q \) and test charge \( q_0 \).
- UP Board XII - 2024
- Gauss’s Law
Compare features of p-type and n-type semiconductors. Draw circuit diagram of half-wave rectifier of p-n junction diode and explain it.
- UP Board XII - 2024
- PN Junction Diode
- There is minimum deviation of light ray on passing through a prism (n = \( \sqrt{3} \)). If the angle of incidence is twice the angle of refraction for this ray, then what will be the angle of prism and the angle of refraction?
- UP Board XII - 2024
- PN Junction Diode
What is atomic model of magnetism? Differentiate between paramagnetic, diamagnetic, and ferromagnetic substances on this basis. Also, give one example of each.
- UP Board XII - 2024
- Refraction Through A Prism
- In a circuit, the equation for alternating voltage \( V \) is represented by \( V = 40 \sin(100 \pi t) \) volt. Here \( t \) is in seconds. Draw the time-voltage (t-V) graph with proper scale for one cycle. Calculate the root mean square value of voltage.
- UP Board XII - 2024
- Magnetic Effects of Current and Magnetism
View More Questions