Question

Find the equation of tangent to the curve 2 3x 4x2 at x = 1

Answer 1

Answer:

If y = 4x^2 - 3x, then y’ = 8x - 3. At the point (1, 1), x = 1, and 8x - 3 = 8(1) - 3 = 5. Thus, the slope of the line tangent to y at (1, 1) is 5. Using the point-slope formula for the equation of a line that passes through (1, 1) with a slope of 5 is given by

y - 1 = 5(x - 1) = 5x - 5. Therefore, the slope-intercept form of the line tangent to y = 4x^2 - 3x through the point (1, 1) is y = 5x - 4.