[ University Calculus / AP exam /IB exam ] Tangent Line Calculation from a Limit Definition (Quiz)

This Video (based on our math blog and class recordings) presents a step-by-step solution to a calculus problem involving the equation of a tangent line to a continuous function, $f(x)$, at a specific point. The problem utilizes the definition of the derivative at a point by framing the slope calculation within a given limit statement. The solution first determines that the point of tangency is $(2, 4)$ by evaluating the function at $x=2$ based on the limit's numerator approaching zero. Next, the slope of the tangent line is found to be $-3$ by relating the given limit to the formal definition of the derivative, $f'(2)$. Finally, the point-slope formula is used to determine the final equation of the tangent line, which is simplified to $y = -3x + 10$, corresponding to choice A. Copyright all rights reserved Full video check Youtube @mathtutor8285