Question

Find the value of x for which the line tangent to the graph of f(x)=5x^2-7x+3 has a tangent line parallel to the line y=-2x+3. Write your answer as a fraction.

a) 1/2
b) 2/3
c) 3/4
d) 4/5

Answer 1

To find the value of x where the line tangent to f(x) = 5x^2 - 7x + 3 is parallel to y = -2x + 3, we set the derivative of f(x), 10x - 7, equal to -2 and solve for x, yielding x = 1/2.

Step-by-step explanation:

To find the value of x for which the line tangent to the graph of f(x) = 5x^2 - 7x + 3 is parallel to the line y = -2x + 3, first we need to determine the slope of the tangent line to f(x). The slope of the given line is -2, so the slope of the tangent line to the graph of f(x) must also be -2 for the lines to be parallel.

We calculate the derivative of f(x) to find the slope of the tangent line at any point x. The derivative of f(x) is f'(x) = 10x - 7. Setting this equal to the slope of the given line, we have 10x - 7 = -2. Solving for x, we get:

• 10x - 7 = -2
• 10x = 5
• x = 5/10
• x = 1/2

Therefore, the correct answer is a) 1/2.