Question

To write the equation of the line tangent to the curve y = ?x at the point (x, y) = (16, 4), we will need the slope of that tangent line and a point on the tangent line. Use the limit definition of derivative to find the slope of the tangent line, m_tan, to y = ?x at x = 16. m_tan = f'(16) = lim_{x ? 16} (f(x) - f(16)) / (x - 16) = lim_{x ? 16} [ ] / (x - 16)

          To write the equation of the line tangent to the curve y = ?x at the point (x, y) = (16, 4), we will need the slope of that tangent line and a point on the tangent line.

Use the limit definition of derivative to find the slope of the tangent line, m_tan, to y = ?x at x = 16.

m_tan = f'(16) = lim_{x ? 16} (f(x) - f(16)) / (x - 16)

= lim_{x ? 16} [ ] / (x - 16)

To write the equation of the line tangent to the curve y = ?x at the point (x, y) = (16, 4), we will need the slope of that tangent line and a point on the tangent line.

Use the limit definition of derivative to find the slope of the tangent line, mtan, to y = ?x at x = 16.

mtan = f'(16) = limx ? 16 (f(x) - f(16)) / (x - 16)

= limx ? 16 [ ] / (x - 16)

Added by Daniel W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

03/25/2022

Step 1

Given function: y = √x Using the limit definition of derivative: f'(x) = lim (h->0) [f(x + h) - f(x)] / h f'(x) = lim (h->0) [√(x + h) - √x] / h f'(x) = lim (h->0) [(√(x + h) - √x) * (√(x + h) + √x)] / h(√(x + h) + √x) f'(x) = lim (h->0) [(x + h) - x] / h(√(x + h) Show more…

Show all steps

Thanks for your feedback!

To write the equation of the line tangent to the curve y = ∑x at the point (x, y) = (16, 4), we will need the slope of that tangent line and a point on the tangent line. Use the limit definition of derivative to find the slope of the tangent line, m_tan, to y = ∑x at x = 16.