Question

question 11 the slope of the tangent line to the parabola y = 2x^2 + 5x + 3 at the point (0,3) is: the equation of this tangent line can be written in the form y = mx + b where m is: and where b is: question help: video

Explanation:

Step1: Find the derivative

The derivative of $y = 2x^{2}+5x + 3$ using the power - rule $(x^n)'=nx^{n - 1}$ is $y'=4x + 5$.

Step2: Calculate the slope

Substitute $x = 0$ into $y'$. So $m=y'(0)=4\times0 + 5=5$.

Step3: Find the y - intercept

The equation of the line is $y=mx + b$. We know the point $(0,3)$ lies on the line. Substituting $x = 0$, $y = 3$ and $m = 5$ into $y=mx + b$, we get $3=5\times0 + b$, so $b = 3$.

Answer:

The slope of the tangent line is $5$.
The value of $m$ is $5$.
The value of $b$ is $3$.