TS EAMCET · Maths · Continuity and Differentiability
Let \(f\) and \(g\) be two differentiable functions satisfying \(g^{\prime}(5)=\frac{3}{4}, g(5)=6\) and \(g=f^{-1}\). Then \(f^{\prime}(6)\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{1}{6}\)
- C \(\frac{2}{3}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
Given, \(g(x)=f^{-1}(x)\) \[ \Rightarrow \quad f[g(x)]=x \] Differentiating \(f^{\prime}[g(x)] \cdot g^{\prime}(x)=1\) \[ f^{\prime}[g(x)]=\frac{1}{g^{\prime}(x)} \] Putting \(x=5\), we get…
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 a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively isTS EAMCET 2025 Medium
- If the equation \(x+y+n=0\) represents a normal to the hyperbola \(\frac{x^2}{6}-\frac{y^2}{2}=1\), then \(n=\)TS EAMCET 2023 Easy
- If \(y=m x+c\) is a common tangent to the parabola \(y^2=4 \sqrt{k} x\) and the circle \(2 x^2+2 y^2=k\) then the product of the slopes of such common tangents isTS EAMCET 2020 Medium
- The centroid of a triangle with vertices and is thenTS EAMCET 2021 Medium
- The locus of a point which divides the line segment joining the focus and any point on the parabola \(y^2=12 x\) in the ratio \(m: n(m+n \neq 0)\) is a parabola. Then the length of the latus rectum of that parabola isTS EAMCET 2025 Medium
- and are subsets of Every element of is mapped to an element of by the rule, thenTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- An example of covalent solid isTS EAMCET 2015 Easy
- \(\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}\) is equal to :TS EAMCET 2006 Easy
- Match the following:
The correct answer isTS EAMCET 2023 Easy - Which one of the following is an isotonic pair of solutions?TS EAMCET 2013 Easy
- A line is passing through the point whose position vector is and parallel to the vector . A plane is passing through the points and parallel to the vector . Then the point where this plane meets the line isTS EAMCET 2018 Hard
- If \(S_1\) and \(S_2\) are the variances of the first \(2 k\) and \(k(k>1)\) natural numbers respectively, then \(\left(S_1 / S_2\right)\) lies in the intervalTS EAMCET 2020 Easy