For the given function, (a) find the slope of the tangent line to the graph at the given point; (b) find the equation of the tangent line. h(x)=7xatx=6 (a) The slope of the tangent line at x=6 is ____.

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For the given function, (a) find the slope of the tangent line to the graph at the given point; (b) find the equation of the tangent line.   h(x)=7xatx=6  (a) The slope of the tangent line at x=6 is ____.

movingsupplyw1 · Accepted Answer

Step 1 The function is given b y h(x)=7xatx=6 To evaluate: (a) The slope of the tangent line to the graph of the function at x=6 (b) The equation of the tangent line to the graph of the function at x=6 (a) Evaluation of the slope The slope of the tangent line to the graph of the function can be evaluat6ed as following m=dhdx∣x=6 =ddx(7x)∣x=6 =−7x2∣x=6 =−762 =−736 Hence, the slope of the tangent line at x=6is−736

Ella Williams · Accepted Answer

(b) Evaluation of the equation of the tangent line The equation of the tangent line can be evaluated as following y−h(6)=m(x−6) ⇒y−76=−736(x−6) ⇒y−76=−73x+76 ⇒y=−736x+76+76 ⇒y=−736x+73 Hence, the equation of the tangent line at x=6 is y=−736x+73

For the given function, (a) find the slope of the

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