Q. 11 - Calculus

Question

Given that f,g,h are functions with values f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1 Calculate

$(3f+4h)\text{'}\left(2\right)$

Step-by-Step Solution

Answer

The value is $(3f+4h)\text{'}\left(2\right)=5$

Step 1: Given information

We are given f(2)=1, g(2)=-4, h(2)=3 and point -derivatives f'(2)=3, g'(2)=0, h'(2)=-1  

Step 2: Compute the given values

We have to find $(3f+4h)\text{'}\left(2\right)$

Which can be simplified as 

$$\begin{gathered} 3f\text{'}\left(2\right)+4h\text{'}\left(2\right) \\ 3\left(3\right)+4(-1) \\ 9-4 \\ =5 \end{gathered}$$

Hence the value is $(3f+4h)\text{'}\left(2\right)=5$