The equation of the tangent to the curve $y=e^x+3x$ at the point where $x=0$ is:

Step-by-step solution

1. 1. Differentiate the function: $y^{\prime }=e^x+3$.
2. 2. Evaluate the slope at $x=0$: $y^{\prime }(0)=e^0+3=1+3=4$.
3. 3. Find the point of tangency: $y(0)=e^0+3\cdot 0=1$, so the point is $(0,1)$.
4. 4. Use point‑slope form: $y-1=4(x-0)\to y=4x+1$.

Concept tested: Tangent to a curve using derivative

Published 4 October 2026 · How this solution was prepared and checked