Question
The values of a for which the function f(x) = sinx - ax + b increases on R are ______.
✓
Answer
The values of a for which the function f(x) = sinx - ax + b increases on R are $(-\infty-1).$
Solution:
The values of a for which the function f(x) = sinx - ax + b increases on R are $(-\infty-1).$
$\because\ \text{f}'(\text{x})=\cos\text{x}-\text{a}$
and $\text{f}'(\text{x})>0\Rightarrow\cos\text{x}>\text{a}$
Since, $\cos\text{x}\in[-1,1]$
$\Rightarrow\ \text{a}<-1\Rightarrow\text{a}\in(-\infty,-1)$
Solution:
The values of a for which the function f(x) = sinx - ax + b increases on R are $(-\infty-1).$
$\because\ \text{f}'(\text{x})=\cos\text{x}-\text{a}$
and $\text{f}'(\text{x})>0\Rightarrow\cos\text{x}>\text{a}$
Since, $\cos\text{x}\in[-1,1]$
$\Rightarrow\ \text{a}<-1\Rightarrow\text{a}\in(-\infty,-1)$
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