Find and simplify each of the following for

Answer:(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6(B) f(x + h) - f(x) = 8xh + 4h² - 6h(C) [tex]\frac{f(x+h)-f(x)}{h}=8x+4h-6[/tex]Step-by-step explanation:* Lets explain how to solve the problem- The function f(x) = 4x² - 6x + 6- To find f(x + h) substitute x in the function by (x + h)∵ f(x) = 4x² - 6x + 6∴ f(x + h) = 4(x + h)² - 6(x + h) + 6- Lets simplify 4(x + h)²∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²- Lets simplify 6(x + h)∵ 6(x + h) = 6(x) + 6(h)∴ 6(x + h) = 6x + 6h∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6- Remember (-)(+) = (-)∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6- Lets find f(x + h) - f(x)∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6∵ f(x) = 4x² - 6x + 6∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)- Remember (-)(-) = (+)∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6- Simplify by adding the like terms∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)∴ f(x + h) - f(x) = 8xh + 4h² - 6h* (B) f(x + h) - f(x) = 8xh + 4h² - 6h- Lets find [tex]\frac{f(x+h)-f(x)}{h}[/tex]∵ f(x + h) - f(x) = 8xh + 4h² - 6h∴ [tex]\frac{f(x+h)-f(x)}{h}=\frac{8xh + 4h^{2}-6h}{h}[/tex]- Simplify by separate the three terms∴ [tex]\frac{f(x+h)-f(x)}{h}=\frac{8xh}{h}+\frac{4h^{2} }{h}-\frac{6h}{h}[/tex]∴ [tex]\frac{f(x+h)-f(x)}{h}=8x+4h-6[/tex]* (C) [tex]\frac{f(x+h)-f(x)}{h}=8x+4h-6[/tex]