Linear Approximation, 1 variable, f(x) = √(x), x=49. 4

Hi, I’m Tom from everystepcalculus.com and everystepphysics.com. This is a linear approximation problem in calculus one generally because one variable and we’re going to read it here because it’s off of a test using your approximation to approximate square root of 49.4.  We’re going to let f of X equals the square root of x and then that can be written as the point-slope form of y equals MX plus B so we’re going to compute m and B.  Let’s do it,  Index 8 to get to my menu. We’re going to scroll down here to linear approximation,  in the L section. And we’re going to use one variable because there’s only x given.  So linear approximation, one variable,  I’m going to use the point-slope form equation for a tangent line to occur y equals MX plus B. We’re going to enter function,  you have to press alpha before you enter anything into these entry lines here.  So it’s alpa and second X will give us the square root sign put in the X close off the parentheses. Press Enter. I always show you what you’ve entered you can change it if you want. We’re going to enter the point but you want to evaluate this at. We’re going to press alpha again and I’m going to pull 49.4. Check that make sure it’s right again. I say it’s okay.  First thing we do is we enter the function and get it do the derivative of that which is the slope and it equals m.   Here’s the derivative of that. And we find that the closest square root number for that given number 49 and we add that into the derivative and so the slope is equal to one over 14.  Now we take that number 49 again and add it into the original function. We came up with y equals seven. So the point is 49 for x and 7 y,  okay. Y equals seven,  then we’re going to find B so we do the calculations here in algebra. And b turns out to be 7 halves . We found that already, ok. If you want to go further and they’re asked for this point slope form this is equal to y equals MX plus B slope times X to speak now we’re going to enter the original point where after in the same formula and so then y is equal to 7.029, okay?  And the XY is 49.4, 7.029.  Pretty neat,huh? everystepcalculus.com. Go to my site, buy my programs, and pass calculus. Have a good one.