Question:
The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)
The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)
Show Hint
The slope of a function at a given point is simply the value of its derivative at that point.
Updated On: Nov 27, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 57
Solution and Explanation
To find the slope, we need to compute the derivative of the function:
\[
f'(x) = \frac{d}{dx}(2x^4 - 3x^2 + 5x) = 8x^3 - 6x + 5
\]
Substitute \( x = 2 \):
\[
f'(2) = 8(2^3) - 6(2) + 5 = 8(8) - 12 + 5 = 64 - 12 + 5 = 57
\]
Thus, the slope at \( x = 2 \) is \( \boxed{57} \).
Was this answer helpful?
0
0
Top Questions on Partial derivatives
- If \( u = x^4 + y^4 + 3x^2 y^2 \), the value of \( \left( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \right)^{-1} \) is:
- GATE AG - 2025
- Engineering Mathematics
- Partial derivatives
If \(u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)\), then the value of \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is:
- TS PGECET - 2024
- Engineering Mathematics
- Partial derivatives
- Consider the following expression: \[ z = \sin(y + it) + \cos(y - it) \] where \( z \), \( y \), and \( t \) are variables, and \( i = \sqrt{-1} \) is a complex number. The partial differential equation derived from the above expression is
- GATE CE - 2022
- Engineering Mathematics
- Partial derivatives
- The surface area of the paraboloid \( z = x^2 + y^2 \) between the planes \( z = 0 \) and \( z = 1 \) is __________ (round off to ONE decimal place).
- GATE MA - 2022
- Calculus
- Partial derivatives
- The work done by the force \( \mathbf{F} = (x + y) \hat{i} - (x^2 + y^2) \hat{j} \),
where \( \hat{i} \) and \( \hat{j} \) are unit vectors in \( \mathbf{O X} \) and \( \mathbf{O Y} \) directions, respectively, along the upper half of the circle \( x^2 + y^2 = 1 \) from \( (1, 0) \) to \( (-1, 0) \) in the \( xy \)-plane is
- GATE MA - 2022
- Calculus
- Partial derivatives
View More Questions
Questions Asked in GATE AG exam
- The series \[ \sum_{n=0}^{r} q^n = 1 + q + q^2 + \cdots + q^r \] has the sum:
- GATE AG - 2025
- geometric progression
- If \(a\), \(b\), and \(c\) are the roots of \( 2x^3 - 3x^2 + px - 1 = 0 \) and the sum of two roots is 1, the value of \(p\) is:
- GATE AG - 2025
- Algebraic Methods of Solving a Pair of Linear Equations
- While sowing mustard seeds (bulk density = 800 kg.m\(^{-3}\)), a four-row fluted roller type seed drill with 25 cm row spacing operates at a speed of 2.5 km.h\(^{-1}\). For a desired seed rate of 5.0 kg.ha\(^{-1}\), the flowrate of seeds from the machine in m\(^3\).h\(^{-1}\) is:
- GATE AG - 2025
- Soil Mechanics
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?- GATE MA - 2025
- GATE AG - 2025
- Blood Relations
View More Questions