So this value on simplifying, we get this advisable to X over six -6-6. Now the slope is given of the normal line would be, the equation of the normal line would be given as y minus zero is equal to the slope which is 1/6 times x minus Ln six. So the slope of this normal line would be given as 1/6 which is just the reciprocal and the negative of the reciprocal of minus six.
Normal line is perpendicular to the tangent line.
Next we have to find the equation of the normal line. So this is the required tangent line equation.
#FIND THE SLOPE OF FX EQUATION PLUS#
So when we solve this, so this is what it's gonna do, Why is going to -6 x Plus 6 6. So this would be why minus zero and the slope is minus six times x minus Ln six. So at this point we have to find the equation of the tangent. X coordinate and this is the y coordinate. It's difficult to add the point and then six comma zero because this is the X. Now, in the second part we have to find the equation of the tangent line at the point. So the slope is equal the required slope is equal to minus six. So this is the required value of the slope. slope (m) - coefficient of x / coefficient of y. If the equation of a line is given general form, we can find the slope of the line using the formula given below. Method 2 : General form equation of a line : y mx + b. Because Edith power Ellen either the power of Ln six is six and this is minus. We can write the equation of a line in slope intercept form and find the slope 'm' which is being as the coefficient of x. So that is equal to minus each with power Ellen six. So now the slope at this point would be F prime Ln six. So that would be zero and each of the power X is differentiated and that is equal to eat the power X only. So here for you first find the derivative which is F prime X is equal to minus E to the power X because six is constant. So F prime of or the first derivative of the function at point X is equal to Ln six. So we have to find their primates at Ln six. So this is six minus, It is about X is equal to zero at that point. So let's find where is the intersection point. So we have to find the the the derivative of that function at that point. So for that if X is equal to zero, so where it causes the X axis. Now here we have to find the slope of this function where it is with respect to X. So in the given problem we are given with the function F X is equal to six minus E.
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