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I am new in differential equation. I just want to solve the following problem,

Can any one give me the step wise solution for this question???

Determine the equation of the tangent line for the function

f(x) = x2 + 1 at point (3,10).

10 years ago

Find the slope of the function by differentiation
f '(x) = 2x

Plug in the certain point's values Since this function does not have y we don't plug in y yet
f '(3) = 6 {6 is now the slope of the point 3,10}

Plug both slope and point values into a linear equation
(y - y1) = m(x - x1) {this is the linear equation}
(y - 10) = 6(x - 3)  {Which can be simplified as below}
y = 6x -8

Just as we can find the slope and equation of a tangent line for a function, we can also do the same for a normal line. However, the normal line has two differences from the tangent line.

1. The slope of a normal line is perpendicular to the slope of the tangent line. Or in other words, the negative inverse of the tangent line.

2. The normal line is only defined if x does not = 0.

As a result, to find the slope and equation of the normal line, follow the steps above and convert the slope of the tangent line to the slope of the normal line.

10 years ago
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