Use the function f(x)=9x−4 find the following. (a) Use the limit definition of the derivative to find f(x). f(x)=? (b) Find the equation of the tangent line at x=5.

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Use the function f(x)=9x−4  find the following.  (a) Use the limit definition of the derivative to find f(x).  f(x)=?  (b) Find the equation of the tangent line at x=5.

enlacamig · Accepted Answer

Step1We have given the functionf(x)=9x−4Step 2(a) Use the limit gefinition of the derivative to find f′(x).Thenlimh⇒0f(x+h)−f(x)h=limh⇒0(9x+h−4−9x−4h)=limh⇒0(9(x−4)−9(h+x−4)(x−4)(h+x−4)h)=limh⇒0(−−9h(x−4)(h+x−4)h)=limh⇒0(−9(x−4)(h+x−4))Step 3While plugging the value h=0, we havelimh⇒0(−9(x−4)(h+x−4))=−9(x−4)(h+x−4)=−9(x−4)2Therefore, f′(x)=−9(x−4)2

Nadine Salcido · Accepted Answer

Step 4 (b) Find the equation of the tangent value at x=5. First find the functional value at x=5. f(5)=−95−4=9 Then find the slope at x=5. f(5)=−9(5−4)2=−9 Step 5 Using point-slope formula for a line using the point (5,f(5))=(5,9), we have y−9=−9(x−5) y−9=−9x+45 y=−9x+54 Step 6 Therefore, the equation of the tangent line at x=5 is y=−9x+54.

Use the function f(x)=\frac{9}{x-4} find the following. (a) Use the limit definition

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