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Use the definition of the derivative to find f'(x).
f(x)=4x²
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3.2 Question 57
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Re: 3.2 Question 57
by Eigenvalue » Wed Sep 23, 2026 6:59 pm
f'(x)=[tex]\lim_{x \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
=[tex]\lim_{x \to 0} \frac{4(x+h)²-4x²}{h}[/tex]
=[tex]\lim_{x \to 0} \frac{4x²+8xh+4h²}{h}[/tex]
=[tex]\lim_{x \to 0}8x+4h[/tex]
=8x
=[tex]\lim_{x \to 0} \frac{4(x+h)²-4x²}{h}[/tex]
=[tex]\lim_{x \to 0} \frac{4x²+8xh+4h²}{h}[/tex]
=[tex]\lim_{x \to 0}8x+4h[/tex]
=8x
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Re: 3.2 Question 57
by nycmath » Wed Sep 23, 2026 9:18 pm
Eigenvalue wrote:f'(x)=[tex]\lim_{x \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
=[tex]\lim_{x \to 0} \frac{4(x+h)²-4x²}{h}[/tex]
=[tex]\lim_{x \to 0} \frac{4x²+8xh+4h²}{h}[/tex]
=[tex]\lim_{x \to 0}8x+4h[/tex]
=8x
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