f(x)=3x^2 find f(a+h)-f(a) / h

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on Jan 13, 2025 at 10:34 am



MathBot Answer:

f(a+h)−f(a)h=3a2h−3a2+6h2a+3h3h\begin{aligned}f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{3 a^{2} h - 3 a^{2} + 6 h^{2} a + 3 h^{3}}{h}\end{aligned}

f(a+h)−f(a)h=3(a+h)2−3a2hf(a+h)−f(a)h=(−3)a2h+3(a+h)2f(a+h)−f(a)h=(−3)a2h+3(a2+2ah+h2)f(a+h)−f(a)h=3a2h−3a2+6h2a+3h3h\begin{aligned}f\left( a + h \right) - \frac{f\left( a \right)}{h}&=3 \left(a + h\right)^{2} - \frac{3 a^{2}}{h}\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{\left(-3\right) a^{2}}{h} + 3 \left(a + h\right)^{2}\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{\left(-3\right) a^{2}}{h} + 3 \left(a^{2} + 2 a h + h^{2}\right)\\f\left( a + h \right) - \frac{f\left( a \right)}{h}&=\frac{3 a^{2} h - 3 a^{2} + 6 h^{2} a + 3 h^{3}}{h}\\\end{aligned}

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