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Tangent Slope Question?
So here's the problem
Graph the Function of f(x)= square root of x on the interval [0,9]. SHow the secant lines passing throught the point (4,2) and theses values of x : 1, 3, 4,5
ok so far I got that graphed and found the slope of eavh secant line
a. 1/3
b. square root 3 +2
c. Square root 5 - 2
Now the problem where im stuck is estimate the slope of the tangent to the curve at the point (4,2)
i don't understand how im suppose to get the answer. Please don't use derivatives. Thank you so much for the help
forget the 4 i put in for the extra values that was a mistake just 1,3,5
1 Answer
- JoergLv 69 years ago
If I understand this right, there are three lines
to be found:
a) passing through (1,?) and (4,2)
b) passing through (3,?) and (4,2)
c) passing through (5,?) and (4,2)
They have the following formulae:
a) y=2/3*x-2/3
b) y=2*x-6
c) y=-2*x+10
The factor of x is the respective slope:
for a)=2/3
for b)=2
for c)=-2
To estimate the slope of the tangent at (4,2)
your aren't too far away with the first slope
which is 2/3.
It appears to be a bit too steep.
You could try to lower it a bit and find
the equation of the tangent line either
passing (4,2) or passing nearby. This way
you could judge from comparing the slopes
visually.
E.g.try:
y=1/3*x+2/3
y=1/4*x+1
It's an estimate, not an exact value.
Hope it helps.