**Finding the Equation of the Tangent Line**The problem requires finding the equation of the tangent line at the point \((1, f(1))\) for the function \(f(x)\), given that \(f(1) = 4\) and \(f'(1) = 3\). The steps to solve this problem are detailed below:---**Problem Statement:**Find the equation of the tangent line at \((1, f(1))\) when \(f(1) = 4\) and \(f'(1) = 3\).*Use symbolic notation and fractions where needed.***Solution:**To find the equation of the tangent line to the function \(f(x)\) at the point \((1, f(1))\):1. We need to use the point-slope form of the equation of a line. 2. The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.3. In this problem, \(x_1 = 1\), \(y_1 = f(1) = 4\), and the slope \(m = f'(1) = 3\).Substituting these values into the point-slope form, we obtain:\[y - 4 = 3(x - 1)\]4. To express this in the slope-intercept form \(y = mx + b\) if needed, solve the equation for \(y\):\[y - 4 = 3x - 3 \implies y = 3x - 3 + 4 \implies y = 3x + 1\]**Equation:**\[y = 3x + 1\]---This equation represents the tangent line to the function \(f(x)\) at the specified point.

Name: **Finding the Equation of the Tangent Line**The problem requires find
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Finding the Equation of the Tangent Line**The problem requires finding the equation of the tangent line at the point \((1, f(1))\) for the function \(f(x)\), given that \(f(1) = 4\) and \(f'(1) = 3\). The steps to solve this problem are detailed b