2/3: QUIZ 5 Sections 3.1, 3.2 YES CRADED $$ \begin{array}{l}\text { Find the equation of the line tangent to the graph of } f \text { at the indicated value of } x \text {. } \ f(x)=15 e^{x}+14 x ; x=0\end{array} $$ $$ y=\square $$

Question

UpStudy AI · Accepted Answer

1. Calculate the value of $$ f(0) $$:
   $$
   f(0) = 15e^0 + 14(0) = 15 \times 1 + 0 = 15.
   $$

2. Compute the derivative $$ f'(x) $$:
   $$
   f'(x) = \frac{d}{dx} \left( 15e^x + 14x \right) = 15e^x + 14.
   $$

3. Evaluate the derivative at $$ x = 0 $$:
   $$
   f'(0) = 15e^0 + 14 = 15 \times 1 + 14 = 29.
   $$

4. Write the equation of the tangent line using the point-slope form:
   $$
   y - f(0) = f'(0)(x - 0) \quad \text{or} \quad y - 15 = 29x.
   $$

5. Solve for $$ y $$:
   $$
   y = 29x + 15.
   $$

$$ y=29x+15 $$
$$ y = 29x + 15 $$

2/3: QUIZ 5 Sections 3.1, 3.2 YES CRADED

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Calculus Questions