Subjects calculus

Tangent Line D9Ded3

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1. The problem asks if finding the equation of the tangent line means finding the derivative. 2. The equation of the tangent line to a curve at a point involves two things: the slope of the tangent line and the point of tangency. 3. The slope of the tangent line is given by the derivative of the function at that point, i.e., if the function is $f(x)$, the slope is $f'(a)$ where $a$ is the x-coordinate of the point. 4. The equation of the tangent line at $x=a$ is given by the point-slope form: $$y - f(a) = f'(a)(x - a)$$ 5. So, finding the equation of the tangent line requires finding the derivative (to get the slope) and then using the point on the curve to write the line equation. 6. Therefore, yes, finding the equation of the tangent line involves finding the derivative, but also using the point to write the full line equation.