Use the limit definition of the derivative to find the slope of the tangent line to the curve \( f(x)=7 x^{2} \) at \( x=3 \) Evaluate each of the following and enter your answers in simplest form: Step 1 \[ f(3+h)= \] \( \square \) Step \( 2 f(3+h)-f(3)= \) \( \square \) Step \( 3 \quad \frac{f(3+h)-f(3)}{h}= \) \( \square \) Step \( 4 \lim _{h \rightarrow 0} \frac{f(3+h)-f(3)}{h}= \) \( \square \) So, \( f^{\prime}(3)= \) \( \square \)
Added by Teodora B.
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\[ f(3+h) = 7(3+h)^2 \] \[ = 7(9 + 6h + h^2) \] (Expanding \( (3+h)^2 \)) \[ = 63 + 42h + 7h^2 \] So, \( f(3+h) = 63 + 42h + 7h^2 \). Show more…
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