Find the maximum and minimum value, f(x) = -(x - 1)^2 + 10 - Vidyadip

Question

Find the maximum and minimum value, $f(x) = -(x - 1)^2 + 10$

✓

Answer

It is given that $f(x) = -(x - 1)^2 + 10$
Now, we can see that $(x - 1)^2 \ge 0$ for every $x \in R$
$\Rightarrow f(x) = -(x - 1)^2 + 10 \le 10$ for every $x \in R$
The maximum value of f is attained when $x - 1 = 0$
i.e, $x - 1 = 0$
$\Rightarrow x = 1$
Then, Maximum value of $f = f(1) = -(1 - 1)^2 + 10 = 10$
Since, $x = 1$ is the only critical point,
Therefore, function f does not have a minimum value.

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 Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the second-order derivative of the function x.cos x

If the vectors $3\hat{\text{i}}+\text{m}\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-\hat{\text{j}}-8\hat{\text{k}}$ are orthonal, find m.

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.

If $\vec{\text{a}}\text{ and }\vec{\text{b}}$ denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
2 Blue balls.

Evaluate the following integrals:$\int\frac{\cos\text{x}}{\sqrt{4-\sin^2\text{x}}}\text{ dx}$

Solve the differential equation $y e^{\frac{x}{y}} d x=\left(x e^{\frac{x}{y}}+y^{2}\right) d y(y \neq 0)$

Evaluate the following integrals:
$\int(\sec^2\text{x}+\text{cosec}^2\text{x})\text{dx}$

If $\begin{vmatrix}2\text{x}+5&3\\5\text{x}+2&9\end{vmatrix}=0,$ find x.

If $\vec{\text{a}}$ is a unit vector, then find $|\vec{\text{x}}|$ in each of the following.$\big(\vec{\text{x}}-\vec{\text{a}}\big).\big(\vec{\text{x}}+\vec{\text{a}}\big)=12$