The tangent to the graph of the function y = 3-2 x ^ 2 is parallel to the straight line y = 4x.

The tangent to the graph of the function y = 3-2 x ^ 2 is parallel to the straight line y = 4x. find the abscissa of the touch point

General view of the equation of the tangent to the function: y = (f (x0)) ‘* x + b. Let’s find the derivative of the given function:

y = (3 – 2x ^ 2) ‘= -4x.

Since the required tangent is parallel to the straight line y = 4x, we get the equation:

-4x = 4;

x = -1.

x0 = -1 is the abscissa of the tangency point, let’s calculate its ordinate:

y (-1) = 3 – 2 (-1) ^ 2 = 3 – 2 = 1.

We substitute the obtained coordinates into the tangent equation and find b:

4 * (-1) + b = 1;

b = 1 + 4 = 5.

Answer: the desired equation of the tangent line at a point looks like this y = 4x + 5.