Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter four, use the limit definition. Pay careful attention to the function names and independent variables. It is important to be comfortable with us- ing letters other than f and x. For example, given a function p(z), we call its derivative p'(z). a. f(x) = 1 e. F(t) = } f. G(y) = Vy c. p(z) = z² b. g(t) = t d. q(s) = s3
Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter four, use the limit definition. Pay careful attention to the function names and independent variables. It is important to be comfortable with us- ing letters other than f and x. For example, given a function p(z), we call its derivative p'(z). a. f(x) = 1 e. F(t) = } f. G(y) = Vy c. p(z) = z² b. g(t) = t d. q(s) = s3
Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter four, use the limit definition. Pay careful attention to the function names and independent variables. It is important to be comfortable with us- ing letters other than f and x. For example, given a function p(z), we call its derivative p'(z). a. f(x) = 1 e. F(t) = } f. G(y) = Vy c. p(z) = z² b. g(t) = t d. q(s) = s3
Please try not to use derivatives or integrals to calculate the stuff. Thank you.
Transcribed Image Text:Activity 1.4.3. For each of the listed functions, determine a formula for the derivative
function. For the first two, determine the formula for the derivative by thinking about
the nature of the given function and its slope at various points; do not use the limit
definition. For the latter four, use the limit definition. Pay careful attention to the
function names and independent variables. It is important to be comfortable with us-
ing letters other than f and x. For example, given a function p(z), we call its derivative
p'(z).
a. f(x) = 1
c. p(z) = z²
e. F(t) =
b. g(t) = t
d. q(s) = s3
f. G(y) = vy
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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