Download App

CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
If $\text{f}:[-5,\ 5]\rightarrow\ \text{R}$ is a differentiable function and if f'(x) does not vanish anywhere, then prove that $\text{f}(-5)\neq\text{f}(5).$
✓

Answer

For, Rolle’s theorem, if
f is continuous is [a, b]
f is derivable in [a, b]
f(a) = f(b)
Then, $\text{f}'\text{(c)}=0,\ \text{c}\in(\text{a},\ \text{b)}$
It is given that f is continuous and derivable, but $\text{f}'\text{(c)}\neq0$
$\Rightarrow\ \text{f(a)}\neq\text{f(b)}$
$\Rightarrow\ \text{f}(-5)\neq\text{f}(5)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Write a unit vector perpendicular to $\hat{\text{i}}+\hat{\text{j}}$ and $\hat{\text{j}}+\hat{\text{k}}.$
→
Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by:$a_{ij} = 2i - j$
→
Write the value of $\sin^{-1}\Big(\frac{1}{3}\Big)-\cos^{-1}\Big(-\frac{1}{3}\Big).$
→
Find the general solution of the differential equation $\frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}$
→
If $\begin{bmatrix}9&-1&4\\-2&1&3 \end{bmatrix}=\text{A}+\begin{bmatrix}1&2&-1\\0&4&9 \end{bmatrix},$ then find matrix A.
→
The following defines a relation on N:
$\text{x} +\text{y} = 10,\text{x, y}\in\text{N}$ $$
Determine which of the above relations are reflexive, symmetric and transitive.
→
Evaluate the following:
$\sec\Big(\sin^{-1}\frac{12}{13}\Big)$
→
Determine P(E|F): A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses.
→
Find the domain of the following functions:
$\text{f(x)}=\sin^{-1}\text{x}^2$
→
If A is a square matrix, then write the matrix adj $(A^T) − (adj\ A)^T$.
→