Maths · Differentiation of the sum, difference, product and quotient of two functions
If defined by =\boldsymbol{2} \boldsymbol{x}^{2}- \) then find the value of -\bo
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}^{2}- \) \( 3 x+5, \) then find the value of \( \frac{\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{h}} \) at \( \boldsymbol{h} \neq \mathbf{0} \)
- A. \( 4 x+2 h \)
- B. \( 4 x+2 h-3 \)
- C. \( 4 x-2 h+3 \)
- D. \( 4 x-2 h-3 \)
Step-by-step solution
Compute f(x+h) = 2(x+h)^2 - 3(x+h) + 5 = 2x^2 + 4xh + 2h^2 - 3x - 3h + 5. Then f(x+h)-f(x) = 4xh + 2h^2 - 3h. Divide by h gives 4x + 2h - 3.