Let f(x) = x² - 6x + 5.
Find the values of x ...

Question

Let f(x) = x² - 6x + 5.

Find the values of x for which the slope of the curve y = f(x) is 0.

Accepted Answer

Welcome back, everyone. In this problem, for the function P of Z E equals Z2 minus 4 Z + 7, identify the value of Z at which the slope of the tangent line to the curve is 0. A says it's at Z equals 1, B2, C3, and the D4. Now if we're going to identify the value of Z at which the slope to the of the tangent line to the curve is zero, we'll need to find the slope of the tangent line. And to get that slope, we can compute the derivative of P Z. So let's differentiate P of Z, set it to zero, and then solve for a Z to find that value. No, give PRC you. Is equal to Z2 minus 4 Z + 7, OK. Then if we differentiate PF Z, we can apply the power rule, OK? And then if we use the power rule here, it tells us that we can bring down the power and subtract one from the term. And when we bring down the power of Z squared, so that's gonna be 2 Z to the 2 minus 1 or the Z to the 1 Z. When we differentiate -4 Z, we end up with -4. And when we differentiate our constant 7, we end up with 0. So the derivative of P of Z equals 2 Z minus 4. OK. Now, at the point. Where the derivative of p of Z is equal to zero, then that must mean that 2 z minus 4 equals 0. In that case, if we add 4 to both sides, 2 z equals 4, and Z equals 4 divided by 2, which is 2. Thus, the value of Z, at which the slope of the tangent line to the curve is 0, is Z equals 2. B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Let f(x) = x2 - 6x + 5.Find the values of x for which the slope of the curve y = f(x) is 0.

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Let f(x) = x² - 6x + 5.
Find the values of x for which the slope of the curve y = f(x) is 0.