Download App

Applications of Derivative — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplications of Derivative2 Marks
Question
What is the maximum value of $a \sin x+b \cos x$ ?
✓

Answer

Suppose
$
\begin{aligned}
y & =a \sin x+b \sin x \\
\frac{d y}{d x} & =a \cos x-b \sin x
\end{aligned}
$
For, maxima and minima $\frac{d y}{d x}=0$$
\begin{array}{l}
\therefore a \cos x-b \sin x=0 \\
\tan x=\frac{a}{b} \\
\frac{d^2 y}{d x^2}=-a \sin x-b \cos x \\
=-(a \sin x+b \cos x)=-ve \\
\therefore \text { maximum value }=\frac{a \times a}{\sqrt{a^2+b^2}}+\frac{b \times b}{\sqrt{a^2+b^2}} \\
=\frac{a^2+b^2}{\sqrt{a^2+b^2}}=\sqrt{a^2+b^2}
\end{array}
$

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" from Applications of Derivative→Applications of Derivative — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4.
→
If I3 denotes identity matrix of order 3 × 3, write the value of its determinant.
→
Write the value of $\big[\hat{\text{i}}-\hat{\text{j }}\hat{\text{j}}-\hat{\text{k }}\hat{\text{k}}-\hat{\text{i}}\big].$
→
For the binary operation multiplication modulo 5 (×5) defined on the set S = {1, 2, 3, 4}. Write the value of (3 ×5 4-1)−1
→
A trust fund has Rs. 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of:
  1. Rs. 1800
  2. Rs. 2000
→
Construct a 2 × 2 matrix A = [aij] whose elements aij are given by:
$\text{a}_\text{ij}=\frac{(2\text{i}-\text{j})^2}{2}$
→
Evaluate the following integrals:
$\int\frac{(\sin^{-1}\text{x})^3}{\sqrt{1-\text{x}^2}}=\text{dx}$
→
Evaluate the following integrals:
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$
→
Find the scalar components and magnitude of the vector joining the points P(x1, y1, z1) and Q(x2, y2, z2).
→
Differentiate the cos (log x + ex), x > 0 w.r.t. x.
→