Given f(x) = 4x^2 – 5x + 3 find

f(x + h) – f(x)

asked by guest
on Sep 19, 2024 at 5:10 pm



You asked:

Evaluate the function \(f\left( x \right) = 4 \cdot {x}^{2} - 5 x + 3\), \(f\left( x + h \right) - f\left( x \right)\).

MathBot Answer:

$$\begin{aligned}f\left( x + h \right) - f\left( x \right)&=4 h^{2} + 8 h x - 5 h\end{aligned}$$

$$\begin{aligned}f\left( x + h \right) - f\left( x \right)&=-\left(3 - 5 x + 4 x^{2}\right) + 3 - 5 \left(h + x\right) + 4 \left(h + x\right)^{2}\\f\left( x + h \right) - f\left( x \right)&=3 - 5 \left(h + x\right) + 4 \left(h + x\right)^{2} + - 4 x^{2} + 5 x - 3\\f\left( x + h \right) - f\left( x \right)&=3 - 5 \left(h + x\right) + 4 \left(h^{2} + 2 h x + x^{2}\right) + - 4 x^{2} + 5 x - 3\\f\left( x + h \right) - f\left( x \right)&=3 - 5 \left(h + x\right) + 4 h^{2} + 8 h x + 4 x^{2} + - 4 x^{2} + 5 x - 3\\f\left( x + h \right) - f\left( x \right)&=- 4 x^{2} + 5 x - 3 + 4 h^{2} + 8 h x - 5 h + 4 x^{2} - 5 x + 3\\f\left( x + h \right) - f\left( x \right)&=4 h^{2} + 8 h x - 5 h\\\end{aligned}$$

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