Find the slope of a line tangent to the curve y=2x^2+4x at the point P(−3,6) by finding the limit of the slopes of the secant lines PQ where Q has x-values −2.5, −2.9, −2.99, and −2.999. Sketch the curve and tangent line

Question

Find the slope of a line tangent to the curve y=2x^2+4x at the point P(−3,6) by finding the limit of the slopes of the secant lines PQ where Q has​ x-values −2.5​, −2.9​, −2.99​, and −2.999. Sketch the curve and tangent line

oobleck · Answer

The secant from (-3,6) to (-2.5,2.5) has slope (2.5-6)/(-2.5+3) = -7 now do the same calculation for the other values.

Find the slope of a line tangent to the curve y=2x^2+4x at the point P(−3,6) by finding the limit of the slopes of the secant lines PQ where Q has​ x-values −2.5​, −2.9​, −2.99​, and −2.999. Sketch the curve and tangent line

Find the slope of a line tangent to the curve y=2x^2+4x at the point P(−3,6) by finding the limit of the slopes of the secant lines PQ where Q has x-values −2.5, −2.9, −2.99, and −2.999. Sketch the curve and tangent line